Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
| Modules | Credits | TAF | SSD |
|---|
2° Year It will be activated in the A.Y. 2025/2026
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
| Modules | Credits | TAF | SSD |
|---|
1 module between the following:
- A.A. 2024/2025 Computational algebra not activated;
- A.A. 2025/2026 Homological Algebra not activated.1 module between the following 3 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Differential geometry (2024/2025)
Teaching code
4S003196
Academic staff
Coordinator
Credits
6
Language
English
Scientific Disciplinary Sector (SSD)
MAT/03 - GEOMETRY
Period
Semester 1 dal Oct 1, 2024 al Jan 31, 2025.
Courses Single
Authorized
Learning objectives
The course aims to provide students with the basic concepts on Differential Geometry of manifolds. At the end of the course the student will know the main terminology and definitions about manifolds and Riemannian manifolds, and some of the main results. He/she will be able to produce rigorous arguments and proofs on these topics and he/she will be able to read articles and texts of Differential Geometry.
Prerequisites and basic notions
Calculus in several variables. Affine and euclidean geometry. Theory of curves and surfaces. Vector fields on Rn and differential forms. Green's theorem, divergence theorem and Stokes' Theorem. Theory of ordinary differential equations.
Program
DIFFERENTIABLE MANIFOLDS
Manifolds, submanifolds, mappings. The Tangent Bundle and vector bundles. Vector fields and flows. Lie derivative and Frobenius' Theorem.
TENSORS CALCULUS
Tensor product of vector spaces, and tensor algebra. Tensor bundles and tensor fields. Lie derivative of a tensor field.
DIFFERENTIAL FORMS
Exterior algebra, determinants, volumes and star Hodge operator. Differential forms, the exterior derivative, interior product and Lie derivative. Introduction to de Rham theory.
RIEMANNIAN GEOMETRY
Covariant derivative , torsion and curvature. The metric tensor, the Riemannian connection and curvature of a Riemannian manifold.
Bibliography
Didactic methods
In-room lectures, team working, homeworks and weekly summary in teams. If necessary, the streaming of the lessons will be activated and/or the recorded lessons of last year will be available.
Learning assessment procedures
The exam is composed of a written test and an optional oral examination.
The oral part is optional, but it becomes mandatory to obtain an assessment greater than 27/30.
Evaluation criteria
Students must show that:
- they know and understand the fundamental concepts and techniques of differential geometry
- they have analytical, abstraction and computational abilities
- they support their argumentation with mathematical rigor.
The written test contains both exercises and theoretical questions.
Criteria for the composition of the final grade
The final assessment is given by the mark of the written part and of the optional oral part.
Exam language
English
